Biostats

Question 1

Adjusted Rate (adjustment)

Answer 1

a summarizing procedure for a statistical measure in which the effects of differences in composition of the populations being compare have been minimized by statistical methods. Often performed on rates or relative risk, commonly because of differing age distributions in populations that are being compared. The mathematical procedure commonly used to adjust rates for age differences is direct or indirect standardization. Example: adjustment by regression analysis and by standardization.

Question 2

Alpha (α)

Answer 2

the probability of a type I error, the error of rejecting a true null hypothesis (declaring a difference exists when it does not)

Question 3

Alternative Hypothesis

Answer 3

1. A supposition, arrived at from observation or reflection, that leads to refutable predictions. 2. Any conjecture cast in a form that will allow it to be tested and refuted.

Question 4

Analysis of Variance (ANOVA)

Answer 4

The separation of variance attributable to one cause from the variance attributable to others. By partitioning the total variance of a set of observations into parts due to particular factors, for example, sex, treatment group, etc, and comparing variances (mean squares) by way of F-tests, differences between means can be assessed. The simplest analysis of this type involves a one-way design, in which N subjects are allocated, usually at random, to the k different levels of a single factor. The total variation in the observations is then divided into a part due to differences between level means (the between groups sum of squares) and a part due to the differences between subjects in the same group (the within groups sum of squares, also known as the residual sum of squares). These terms are usually arranged as an analysis of variance table.

If the means of the populations represented by the factor levels are the same, then within the limits of random variations, the between groups mean square and within groups mean square, should be the same. Whether this is so can, if certain assumptions are met, be assessed by a suitable F-test are that the response variable is normally distributed in each population and that the populations have the same variance. Essentially an example of a generalized linear model with an identity link function and normally distributed errors.

Question 5

Bayes’ theorem

Answer 5

A procedure for revising and updating the probability of some event in the light of new evidence. The theorem originates in an essay by the Reverend Thomas Bayes. In its simplest form the theorem may be written in terms of conditional probabilities as,

pr (Bj| A)=

where Pr( A | Bj ) denotes the conditional probability of event A conditional on event Bj and B1 , B2 ,…,Bk are mutually exclusive and exhaustive events. The theorem gives the probabilities of the Bj when A is known to have occurred. The quantity Pr( Bj ) is termed the prior probability and Pr( Bj | A ) the posterior probability . Pr( A | Bj ) is equivalent to the (normalized) likelihood , so that the theorem may be restated as posterior (prior) x (likelihood).

Question 6

Beta (β)

Answer 6

The probability of a type II error, the error of failing to reject a false null hypothesis, i.e. declaring that a difference does not exist when in fact it does.

Question 7

Bias

Answer 7

In general terms, deviations of results or inferences from the truth, or processes leading to such deviation. More specifically, the extent to which the statistical method used in a study does not estimate the quantity thought to be estimated, or does not test the hypothesis to be tested. In estimated usually measured by the difference between a parameter estimate and its expected value. An estimator for which is said to be unbiased .

Question 8

Binary Variable (Binary Observation)

Answer 8

Observations which occur in one of two possible states, these often being labeled 0 and I. Such data is frequently encountered in medical investigations; commonly occurring examples include ‘dead/alive’, ‘improved/not improved’ and ‘depressed/not depressed.’ Data involving this type of variable often require specialized techniques for their analysis such as logical regression.

Question 9

Binomial Distribution

Answer 9

The distribution of the number of ‘successes’, X, in a series of n- independent Bernoulli trials where the probability of success at each trial is p and the probability of failure is q = 1- p . Specifically the distribution is given by

Pr(X=x) = n!/x!(n-x)![q^(n-x)], x = 0, 1, 2 ……, n

The mean, variance, skewness and kurtosis of the distribution are as follows: 
mean = np 
variance = npq 
skewness = ( q - p )/( npq ) 1/2 
kurtosis = 3-(6/n)+1/npq

Question 10

Biostatistics

Answer 10

A branch of science which applies statistical methods to biological problems. The science of biostatistics encompasses the design of biological experiments, especially in medicine and health sciences.

Question 11

Bivariate

Answer 11

outcomes belong to two categories, e.g. yes/no, acceptable/defective “bivariate binomial distribution”.

Question 12

Blinded Study (Blinding)

Answer 12

A procedure used in clinical trials to avoid the possible bias that might be introduced if the patient and/or doctor knew which treatment the patient is receiving. If neither the patient nor doctor are aware of which treatment has been given the trial is termed double-blind. If only one of the patient or doctor is unaware, the trial is called single-blind. Clinical trials should use the maximum degree of blindness that is possible, although in some areas, for example, surgery, it is often impossible for an investigation to be double-blind.

Question 13

Bonferroni correction

Answer 13

A procedure for guarding against an increase in the probability of a type I error when performing multiple significance tests. To maintain the probability of a type I error at some selected value (α), each of the m tests to be performed is judged against a significance level (α/m ). For a small number of simultaneous tests (up to five) this method provides a simple and acceptable answer to the problem of multiple testing. It is however highly conservative and not recommended if large numbers of tests are to be applied, when one of the many other multiple comparison procedures available is generally preferable.

Question 14

Case-Control Study

Answer 14

(Syn: case comparison study, case compeer study, case history study, case referent study, retrospective study) The observational epidemiologic study of persons with the disease (or other outcome variable) of interest and a suitable control (comparison, reference) group of persons without the disease.

Question 15

Categorical Data

Answer 15

Categorical data represent types of data which may be divided into groups. Examples of categorical variables are race, sex, age group, and educational level. While the latter two variables may also be considered in a numerical manner by using exact values for age and highest grade completed, it is often more informative to categorize such variables into a relatively small number of groups.

Question 16

Censored Information

Answer 16

An observation (Xi) on some variable of interest is said to be censored if it is known only that Xi =Li ( left-censored) or Xi =Ui ( right-censored) where Li and Ui are fixed values. Such observations arise most frequently in studies where the main purpose variable is time until a particular event occurs (for example, time to death) when at the completion of the study, the event of interest has not happened to a number of subjects.

Question 17

Central Limit Theorem

Answer 17

If a random variable Y has population mean µ and population variance σ2, then the sample mean, , based on n observations, has an appropriate normal distribution with a mean µ and variance σ2/ n , for sufficiently large n. The theorem occupies an important place in statistical theory. In short, the Central Limit Theorem states that if the sample size is large enough, the distribution of sample means can be approximated by a normal distribution, even if the original population is not normally distributed.

Question 18

Chi-Square Distribution

Answer 18

The Chi-Square distribution is based on a normally distributed population with variance σ2, with randomly selected independent samples of size n and computed sample variance s2 for each sample. The sample statistic X2= ( n – 1) s2/σ2. The chi-square distribution is skewed, the values can be zero or positive but not negative, and it is different for each number of degrees of freedom. Generally, as the number of degrees of freedom increases, the chi-square distribution approaches a normal distribution.

Question 19

Chi-square statistic

Answer 19

A statistic having, at least approximately, a chi-squared distribution.

Question 20

Chi-square test for trend

Answer 20

A test applied to a two-dimensional contingency table in which one variable has two categories and the other has k ordered categories, to assess whether there is a difference in the trend of the proportions in the two groups. The result of using the ordering in this way is a test that is more powerful than using the chi-squared statistic to test for independence.

Question 21

clinical trial (phases 1-4)

Answer 21

Syn: therapeutic trial) A research activity that involves the administration of a test regimen to humans to evaluate its efficacy and safety. The term is subject to wide variation in usage, from the first use in humans without any control treatment to a rigorously designed and executed experiment involving test and control treatments and randomization. Several phases of clinical trials are distinguished:

Phase I trial Safety and pharmacologic profiles. The first introduction of a candidate vaccine or a drug into a human population to determine its safety and mode of action. In drug trials, this phase may include studies of dose and route of administration. Phase I trials usually involve fewer than 100 healthy volunteers.

Phase II trial Pilot efficacy studies. Initial trial to examine efficacy usually in 200 to 500 volunteers; with vaccines, the focus is on immunogenicity, and with drugs, on demonstration of safety and efficacy in comparison to other existing regimens. Usually but not always, subjects are randomly allocated to study and control groups.

Phase III trial Extensive clinical trial. This phase is intended for complete assessment of safety and efficacy. It involves larger numbers, perhaps thousands, of volunteers, usually with random allocation to study and control groups, and may be a multicenter trial.

Phase IV trial With drugs, this phase is conducted after the national drug registration authority (e.g., the Food and Drug Administration in the United States) has approved the drug for distribution or marketing. Phase IV trials may include research designed to explore a specific pharmacologic effect, to establish the incident of adverse reactions, or to determine the effects of long-term use. Ethical review is required for phase IV clinical trials, but not for routine post marketing surveillance.

Question 22

coefficient of variation (CV)

Answer 22

he measure of spread for a set of data defined as
100 x standard deviation / mean
CV = s/x bar(100) = sample
CV = σ/µ(100) = population

Originally proposed as a way of comparing the variability in different distributions, but found to be sensitive to errors in the mean. Simpler definition: The ratio of the standard deviation to the mean. This is meaningful only if the variable is measured on a ratio scale.

Question 23

Cohort Study

Answer 23

(Syn: concurrent, follow-up, incidence, longitudinal, prospective study) The analytic method of epidemiologic study in which subsets of a defined population can be identified who are, have been, or in the future may be exposed or not exposed, or exposed in different degrees, to a factor or factors hypothesized to influence the probability of occurrence of a given disease or other outcome.

Question 24

complementary event

Answer 24

Mutually exclusive events A and B for which Pr(A) + Pr(B) = 1
where Pr denotes probability.

Question 25

conditional probability

Answer 25

The probability that an event occurs given the outcome of some other event. Usually written, Pr(A l B). For example, the probability of a person being colour blind given that the person is male is about 0.1, and the corresponding probability given that the person is female is approximately 0.0001. It is not, of course, necessary that Pr(A l B) = Pr(A l B); the probability of having spots given that a patient has measles, for example, is very high, the probability of measles given that a patient has spots is, however, much less. If Pr(A l B) = Pr(A l B) then the events A and B are said to be independent.

Question 26

confidence interval (CI)

Answer 26

A range of values, calculated from the sample observations, that is believed, with a particular probability, to contain the true value of a population parameter. A 95% confidence interval, for example, implies that were the estimation process repeated again and again, then 95% of the calculated intervals would be expected to contain the true parameter value. Note that the stated probability level refers to properties of the interval and not to the parameter itself which is not considered a random variable.

Question 27

confounding variable

Answer 27

an extraneous variable in a statistical model that correlates (positively or negatively) with both the dependent variable and the independent variable . The methodologies of scientific studies therefore need to control for these factors to avoid what is known as a type 1 error : A ‘false positive’ conclusion that the dependent variables are in a causal relationship with the independent variable . Such a relation between two observed variables is termed a spurious relationship . Thus, confounding is a major threat to the validity of inferences made about cause and effect, i.e. internal validity , as the observed effects should be attributed to the confounder rather than the independent variable. By definition, a confounding variable is associated with both the probable cause and the outcome. The confounder is not allowed to lie in the causal pathway between the cause and the outcome: If A is thought to be the cause of disease C, the confounding variable B may not be solely caused by behaviour A; and behaviour B shall not always lead to behaviour C. An example: Being female does not always lead to smoking tobacco, and smoking tobacco does not always lead to cancer. Therefore, in any study that tries to elucidate the relation between being female and cancer should take smoking into account as a possible confounder. In addition, a confounder is always a risk factor that has a different prevalence in two risk groups (e.g. females/males). (Hennekens, Buring & Mayrent, 1987).

Question 28

contingency table (two-way frequency table)

Answer 28

The table arising when observations on a number of categorical variables are cross-classified. Entries in each cell are the number of individuals with the corresponding combination of variable values. Most common are two-dimensional tables involving two categorical variables.

The analysis of such two-dimensional tables generally involves testing for the independence of the two variables using the familiar chi-squared statistics. Three- and higher-dimensional tables are now routinely analyzed using log-linear models.

Question 29

continuous data

Answer 29

result from infinitely many possible values that correspond to some continuous scale that covers a range of values without gaps, interruptions or jumps, e.g. blood pressure.

Question 30

controlled trial

Answer 30

A Phase III clinical trial in which an experimental treatment is compared with a control treatment, the latter being either the current standard treatment or a placebo.

Question 31

correlation coefficient r (Pearson product moment)

Answer 31

An index that quantifies the linear relationship between a pair of variables. In a bivariate normal distribution, for example, the parameter, p. An estimator of p obtained from n sample values of the two variables of interest, (x1, y1), (x2, y2),…,(xn,yn), is Pearson’s product moment correlation coefficient, r, given by

The coefficient takes values between -1 and 1, with the sign indicating the direction of the relationship and the numerical magnitude its strength. Values of -1 and 1 indicate that the sample values fall on a straight line. A value of zero indicates the lack of any linear relationship between the two variables.

Question 32

covariate

Answer 32

Often used simply as an alternative name for explanatory variables, but perhaps more specifically to refer to variables that are not of primary interest in an investigation, but are measured because it is believed that they are likely to affect the response variable and consequently need to be included in analyses and model building.

Question 33

cox regression model (Proportional Hazards Model)

Answer 33

A statistical model used in survival analysis developed by D.R. Cox in 1972 asserting that the effect of the study factors on the hazard rate in the study population is multiplicative and does not change over time.

Question 34

critical value

Answer 34

The value with which a statistic calculated from sample data is compared in order to decide whether a null hypothesis should be rejected. The value is related to the particular significance level chosen.

Question 35

crossover rate

Answer 35

The proportion of patients in a clinical trial transferring from the treatment decided by an initial random allocation to an alternative one.

Question 36

cross-sectional study

Answer 36

(Syn: disease frequency survey, prevalence study) A study that examines the relationship between diseases (or other health-related characteristics) and other variables of interest as they exist in defined population at one particular time.

Question 37

cumulative frequency distribution

Answer 37

The tabulation of a sample of observations in terms of numbers falling below particular values. The empirical equivalent of the cumulative probability distribution. An example of such a tabulation is shown below.

Question 38

degrees of freedom

Answer 38

An elusive concept that occurs throughout statistics. Essentially the term means the number of independent units of information in a sample relevant to the estimation of a parameter or calculation of a statistic. For example, in a two-by-two contingency table with a given set of marginal totals, only one of the four cell frequencies is free and the table has therefore a single degree of freedom. In many cases the term corresponds to the number of parameters in a model. Also used to refer to a parameter of various families of distributions, for example, Student’s t-distribution and the F-distribution.

Question 39

dependent variable (response or outcome variable)

Answer 39

The variable of primary importance in investigations since the major objective is usually to study the effects of treatment and/or other explanatory variables on this variable and to provide suitable models for the relationship between it and the explanatory variables.

Question 40

descriptive statistics

Answer 40

A general term for methods of summarizing and tabulating data that make their main features more transparent. For example, calculating means and variances and plotting histograms.

Question 41

dichotomous observation

Answer 41

A nominal measure with two outcomes (examples are gender male or female; survival yes or no); also called binary. See dichotomous data.

Question 42

dichotomous scale

Answer 42

one that arranges items into either of two mutually exclusive categories, e.g. yes/no, alive/dead.

Question 43

discrete data

Answer 43

result when the number of possible values is either a finite number or a “countable” number.

Question 44

Discrete variable

Answer 44

a countable and finite variable, for example grade:

1, 2, 3, 4…- 12.

Question 45

distribution (population)

Answer 45

In statistics this term is used for any finite or infinite collection of ‘units’, which are often people but may be, for example, institutions, events, etc.

Question 46

double-blinded trial

Answer 46

A procedure used in clinical trials to avoid the possible bias that might be introduced if the patient and/or doctor knew which treatment the patient is receiving. If neither the patient nor doctor are aware of which treatment has been given the trial is termed double-blind.

Question 47

dummy coding

Answer 47

Dummy coding provides one way of using categorical predictor variables in various kinds of estimation models (see also effect coding), such as, linear regression. Dummy coding uses only ones and zeros to convey all of the necessary information on group membership.
http://www.ats.ucla.edu/stat/mult_pkg/faq/general/dummy.htm

Question 48

dummy variable (indicator variable)

Answer 48

in statistics, a variable taking only one of two possible values, one (usually 1) indicating the presence of a condition, and the other (usually 0) indicating the absence of the condition, used mainly in regression analysis.

Question 49

effect or effect size

Answer 49

a measure of the strength of the relationship between two variables. In scientific experiments, it is often useful to know not only whether an experiment has a statistically significant effect, but also the size of any observed effects. In practical situations, effect sizes are helpful for making decisions. Effect size measures are the common currency of meta-analysis studies that summarize the findings from a specific area of research.

Question 50

Effective sample size

Answer 50

The sample size after dropouts, deaths and other specified exclusions from the original sample.

Question 51

expected frequencies

Answer 51

A term usually encountered in the analysis of contingency tables. Such frequencies are estimates of the values to be expected under the hypothesis of interest. In a two-dimensional table, for example, the values under independence are calculated from the product of the appropriate row and column totals divided by the total number of observations.

Question 52

experiment (in probability)

Answer 52

A probability experiment involves performing a number of trials to measure the chance of the occurrence of an event our outcome.
http://www.uic.edu/classes/upp/upp503/sanders4-5.pdf

Question 53

experiment

Answer 53

study in which the investigator intentionally alters one or more factors under controlled conditions in order to study the effects of doing so.

Question 54

explanatory variable

Answer 54

The variables appearing on the right-hand size of the equations defining, for example, multiple regression or logistic regression, and which seek to predict or ‘explain’ the response variable. Also commonly known as the independent variables, although this is not to be recommended since they are rarely independent of one another.

Question 55

factor

Answer 55

An event, characteristic, or other definable entity that brings about a change in a health condition or other defined outcome.

Question 56

factor analysis

Answer 56

A set of statistical methods for analyzing the correlations among several variables in order to estimate the number of fundamental dimensions that underlie the observed data and to describe and measure those dimensions. Used frequently in the development of scoring systems for rating scales and questionnaires.

Question 57

factorial designs

Answer 57

Designs which allow two or more questions to be addressed in an investigation. The simplest factorial design is one in which each of two treatments or interventions are either present or absent, so that subjects are divided into four groups; those receiving neither treatment, those having only the first treatment, those having only the second treatment and those receiving both treatments. Such designs enable possible interactions between factors to be investigated. A very important special case of a factorial design is that where each of k factors of interest has only two levels; these are usually known as 2kfactorial designs. A single replicate of a 2kdesign is sometimes called an unreplicated factorial.

Question 58

false-negative

Answer 58

The proportion of cases in which a diagnostic test indicates disease is absent in patients who have the disease.

v

Question 59

false-positive

Answer 59

The proportion of cases in which a diagnostic test indicates disease is present in disease-free patients.

Question 60

F distribution (variance ratio distribution)

Answer 60

The distribution of the ratio of two independent quantities each of which is distributed like a variance in normally distributed samples. So named in honor of R.A. Fisher who first described the distribution.

Question 61

Fisher’s exact test

Answer 61

An alternative procedure to use of the chi-squared statistic for assessing the independence of two variables forming a two-by-two contingency table particularly when the expected frequencies are small. The method consists of evaluating the sum of the probabilities associated with the observed table and all possible two-by-two tables that have the same row and column totals as the observed data but exhibit more extreme departure from independence. The probability of each table is calculated from the hypergeometric distribution.

Question 62

Fisher’s z-transformation

Answer 62

A transformation of Pearson’s product moment correlation coefficient, r, given by

z = 1/2 1n[(1+r)/(1-r)]

The statistic z has a normal distribution with mean

1/2 1n[(1+p)/(1-p)]

where ? is the population correlation value and variance 1/( n -3) where n is the sample size. The transformation may be used to test hypotheses and to contrast confidence intervals for ?.

Question 63

frequency (occurrence)

Answer 63

a general term describing the frequency or occurrence of a disease or other attribute or event in a population without distinguishing between incidence and prevalence.

Question 64

frequency distribution

Answer 64

lists data values (either individually or by groups of intervals), along with their corresponding frequencies (or counts).

Question 65

frequency table

Answer 65

a way of summarizing data; used as a record of how often each value (or set of values) of a variable occurs. A frequency table is used to summarize categorical, nominal, and ordinal data. It may also be used to summarize continuous data once the data is divided into categories.

Question 66

F-test

Answer 66

A test for the equality of the variances of two populations having normal distributions, based on the ratio of the variances of a sample of observations taken from each. Most often encountered in the analysis of variance , where testing whether particular variances are the same also test for the equality of a set of means.

Question 67

gold standard trials

Answer 67

A term usually retained for those clinical trials in which there is random allocation to treatments, a control group and double-blinding.

Question 68

goodness of fit

Answer 68

Degree of agreement between an empirically observed distribution and a mathematical or theoretical distribution.

Question 69

goodness-of-fit test

Answer 69

A statistical test of the hypothesis that data have been randomly sampled or generated from a population that follows a particular theoretical distribution or model. The most common such tests are chi-square tests.

Question 70

hazard

Answer 70

Inherent capability of an agent or situation to have an adverse effect. A factor or exposure that may effect adversely effect health.

Question 71

hazard rate (force of morbidity, instantaneous incidence rate)

Answer 71

A theoretical measure of the risk of an occurrence of an event, e.g. death or new disease, at a point in time, t , defined mathematically as the limit, as Δ t approaches zero, of the probability that an individual well at time t will experience the event by t + Δ t , divided by Δ t .

Question 72

histogram

Answer 72

A graphical representation of a set of observations in which class frequencies are represented by the areas of rectangles centred on the class interval. If the latter are all equal, the heights of the rectangles are also proportional to the observed frequencies. A histogram of heights of elderly women is shown (see below).

Question 73

historical controls

Answer 73

A group of patients treated in the past with a standard therapy, used as the control group for evaluating a new treatment on current patients. Although used fairly frequently in medical investigations, the approach is not to be recommended since possible biases, due to other factors that may have changed over the time, can never be satisfactory eliminated.

Question 74

homogeneity (homogeneous)

Answer 74

A term that is used in statistics to indicate the equality of some quantity of interest (most often a variance), in a number of different groups, populations, etc.

Question 75

homoscedasticity

Answer 75

homo means “same” and –scedastic means “scattered” therefore homoscedasticity means the constancy of the variance of a measure over the levels of the factors under study.

Question 76

hypothesis testing

Answer 76

A general term for the procedure of assessing whether sample data is consistent or otherwise with statements made about the population.

Question 77

incidence

Answer 77

A measure of the rate at which people without a disease develop the disease during a specific period of time. Calculated as

incidence = # new cases over a period of time/population at risk in the time period

it measures the appearance of disease. More generally, the number of new events, e.g. new cases of a disease in a specified population, within a specified period of time. The term incidence is sometimes wrongly used to denote incidence rate.

Question 78

Independence

Answer 78

Two events are said to be independent if the occurrence of one is in no way predictable from the occurrence of the other. Two variables are said to be independent if the distribution of values of one is the same for all values of the other.

Question 79

independent variable (explanatory variables)

Answer 79

The variables appearing on the right-hand side of the equations defining, for example, multiple regression or logistic regression, and which seek to predict or ‘explain’ the response variable. Using the term independent variable is not recommended since they are rarely independent of one another.

Question 80

inference (statistical)

Answer 80

The process of drawing conclusions about a population on the basis of measurements or observations made on a sample of individuals for the population.

Question 81

interaction

Answer 81

A term applied when two (or more) explanatory variables do not act independently on a response variable. The graphic below shows an example from a 2 x 2 factorial design. In statistics, interaction is also the necessity for a product term in a linear model.

Question 82

intercept

Answer 82

The parameter in an equation derived from a regression analysis corresponding to the expected value of the response variable when all the explanatory variables are zero.

Question 83

interquartile range

Answer 83

A measure of spread given by the difference between the first and third quartiles of a sample.

Question 84

Inter-rater reliability (observer variation, inter-rater agreement, Concordance)

Answer 84

the degree of agreement among raters. It gives a score of how much homogeneity or consensus there is in the ratings given by judges. It is useful in refining the tools given to human judges, for example by determining if a particular scale is appropriate for measuring a particular variable. If various raters do not agree, either the scale is defective or the raters need to be re-trained. There are a number of statistics which can be used to determine inter-rater reliability. Different statistics are appropriate for different types of measurement. Some options are: joint-probability of agreement, Cohen’s kappa and the related Fleiss’ kappa, inter-rater correlation, concordance correlation coefficient and intra-class correlation.

Question 85

intervention study

Answer 85

A study in which conditions are under the direct control of the investigator. In epidemiology, a study in which a population is selected for a planned trial of a regimen whose effects are measured by comparing the outcome of the regimen in the experimental group with the outcome of another regimen in a control group.

Question 86

Kaplan-Meier estimate (product limit method)

Answer 86

A nonparametric method of compiling life or survival tables. This combines calculated probabilities of survival and estimates to allow for censored observations, which are assumed to occur randomly. The intervals are defined as ending each time an event (death, withdrawal) occurs and are therefore unequal.

Question 87

Kappa

Answer 87

A measure of the degree of nonrandom agreement between observers or measurements of the same categorical variable
K=Po–Pe/1-Pe
where Po is the proportion of times the measurements agree, and Pe is the proportion of times they can be expected to agree by chance alone. If the measurements agree more often than expected by chance, kappa is positive; if concordance is complete, kappa = 1; if there is no more nor less than chance concordance, kappa = 0; if the measurements disagree more than expected by chance, kappa is negative.

Question 88

kurtosis

Answer 88

the extent to which a unimodal distribution is peaked.

Question 89

least squares

Answer 89

A principle of estimation, attributable to Gauss, in which the estimates of a set of parameters in a statistical model are those quantities that minimize the sum of squared differences between the observed values of the dependent variable and the values predicted by the model.

Question 90

level of significance

Answer 90

The level of probability at which it is agreed that the null hypothesis will be rejected. Conventionally set at 0.05.

Question 91

life table analysis

Answer 91

A procedure often applied in prospective studies to examine the distribution of mortality and/or morbidity in one or more diseases in a cohort study of patients over a fixed period of time. For each specific increment in the follow-up period, the number entering the period, the number leaving during the period, and the number either dying from the disease (mortality) or developing the disease (morbidity), are all calculated. It is assumed that an individual not completed the follow-up period is exposed for half this period, thus enabling the data for those ‘leaving’ and those ‘staying’ to be combined into an appropriate denominator for the estimation of the percentage dying from or developing the disease. The advantage of this approach is that all patients, not only those who have been involved for an extended period, can be included in the estimation process.

Question 92

likelihood function

Answer 92

A function constructed from a statistical model and a set of observed data that gives the probability of the observed data for various values of the unknown model parameters. The parameter values that maximize the probability are the maximum likelihood estimates of the parameters.

Question 93

likelihood ratio

Answer 93

The ratio of the likelihood of observing data under actual conditions, to observing these data under the other, e.g., “ideal” conditions; or comparison of various model conditions to assess which model provides the best fit. Likelihood ratios are used to appraise screening and diagnostic tests in clinical epidemiology.

Question 94

likelihood ratio test

Answer 94

A statistical test based on the ratio of the maximum value of the likelihood function under one statistical model to the maximum value under another statistical model; the models differ in that one includes and the other excludes one or more parameters.

Question 95

linear regression (of Y on X)

Answer 95

a form of regression analysis in which observational data are modeled by a function which is a linear combination of the model parameters and depends on one or more independent variables. In simple linear regression the model function represents a straight line. The results of data fitting are subject to statistical analysis. The data consist of m values taken from observations of the dependent variable (response variable) y . The independent variables are also called regressors, exogenous variables, input variables and predictor variables. In simple linear regression the data model is written as yi = ß0 + xiß1+ εi where εi is an observational error. ß0 (intercept) and ß1 (slope) are the parameters of the model.

Question 96

logistic regression

Answer 96

A form of regression analysis used when the response variable is a binary variable.The method is based on the logistic transformation or logit of a proportion, namely

logit(p) = ln(p/(1-p))

As p tend to O, logit ( p ) tends to -∞ and as p tends to 1, logit (p) tends to ∞. The function logit (p) is a sigmoid curve that is symmetric about p = 0.5. Applying this transformation, this form of regression is written as;

ln(p/(1-p))= ß0 + ß1x1+…+ ßqxq

where p = Pr(dependent variable=1) and x1, x2,,,, xq are the explanatory variables. Using the logistic transformation in this way overcomes problems that might arise if p was modeled directly as a linear function of the explanatory variables, in particular it avoids fitted probabilities outside the range (0,1). The parameters in the model can be estimated by maximum likelihood estimation.

Question 97

logistic Model

Answer 97

A statistical model of an individual’s risk (probability of disease y ) as a function of a risk factor x :
P( y | x ) = 1/(1 + e -a-βx) where e is the (natural) exponential function. This model has a desirable range, 0 to 1, and other attractive statistical features. In the multiple logistic model, the term βx is replaced by a linear term involving several factors, e.g., β1 x1 + β2 x2 if there are two factors x1 and x2.

Question 98

logit (log-odds)

Answer 98

the logarithm of the ratio of frequencies of two different categorical outcomes such as healthy versus sick.

Question 99

logit model

Answer 99

A linear model for the logit (natural log of the odds) of disease as a function of a quantitative factor X:
Logit (disease given X = x ) = α + β x
This model is mathematically equivalent to the logistic model.

Question 100

log-linear model

Answer 100

A statistical model that uses an analysis of variance type of approach for the modeling of frequency counts in contingency tables.

Question 101

logrank test

Answer 101

A test for comparing two or more sets of survival times, to assess the null hypothesis that there is no difference in the survival experience of the individuals in the different groups

Question 102

longitudinal study (cohort study)

Answer 102

Studies that give rise to longitudinal data. The defining characteristic of such a study is that subjects are measured repeatedly through time.

Question 103

Mantel-Haenszel estimate

Answer 103

Mantel and Haenszel provided an adjusted odds ratio as an estimate of relative risk that may be derived from grouped and matched sets of data. It is now known as the Mantel-Haenszel estimate. The statistic may be regarded as a type of weighted average of the individual odds ratios, derived from stratifying a sample into a series of strata that are internally homogeneous with respect to confounding factors. The Mantel-Haenszel summarization method can also be extended to the summarization of rate ratios and rate differences from follow-up studies. An estimator of the assumed common odds ratio in a series of two-by-two contingency tables arising from different populations, for example, occupation, country of origin, etc.

Question 104

Mantel-Haenszel test

Answer 104

A summary chi-square test developed by Mantel and Haenszel for stratified data and used when controlling for confounding.

Question 105

Marginals

Answer 105

the row and column totals of a contingency table.

Question 106

matching (or matched groups)

Answer 106

The process of making a study group and a comparison group comparable with respect to extraneous factors. Often used in retrospective studies when selecting cases and controls to control variation in a response variable due to sources other than those immediately under investigation. Several kinds of matching can be identified, the most common of which is when each case is individually matched with a control subject on the matching variables, such as age, sex, occupation, etc. When the variable on which the matching takes place is continuous it is usually transformed into a series of categories (e.g. age), but a second method is to say that two values of the variable match if their difference lies between defined limits. This method is known as caliper matching. Also important is group or category matching in which the distributions of the extraneous factors are made similar in the groups to be compared.

Question 107

maximum likelihood estimate

Answer 107

the value for an unknown parameter that maximizes the probability of obtaining exactly the data that were observed. Used to solve logistic regression.

Question 108

McNemar test

Answer 108

A test for comparing proportions in data involving paired samples. The test statistic is given by

x^2 = [(b-c)^2]/(b+c)

where b is the number of pairs for which the individual receiving treatment A has a positive response and the individual receiving treatment B does not, and c is the number of pairs for which the reverse is the case. If the probability of a positive response is the same in each group, then X2 has a chi-squared distribution with a single degree of freedom.

Question 109

mean

Answer 109

A measure of location or central value for a continuous variable. For a definition of the population value see expected value.

Question 110

mean-squared error

Answer 110

the expected value of the square of the difference between an estimator and the true value of a parameter. If the estimator is unbiased then the mean squared error (MSE) is simply the variance of the estimator. For a biased estimator the MSE is equal to the sum of the variance and the square of the bias.

Question 111

Measurement error

Answer 111

A mismatch between an estimated value and its true value. Can be observed when using multiple measures of the same entity or concept.

Question 112

measurement scale

Answer 112

the range of possible values for a measurement (e.g. the set of possible responses to a question, the physically possible range for a set of body weights). Measurement scales can be classified according to the quantitative character of the scale:

dichotomous scale – one that arranges items into either of two mutually exclusive categories, e.g. yes/no, alive/dead.
nominal scale – classification into unordered qualitative categories, e.g. race, religion, country of birth. Measurements of individual attributes are purely nominal scales, as there is no inherent order to their categories.
ordinal scale – classification into ordered qualitative categories, e.g. grade, where the values have a distinct order but their categories are qualitative in that there is no natural (numerical) distance between their possible values.
interval scale –an equal interval involves assignment of values with a natural distance between them, so that a particular distance (interval) between two values in another region of the scale. Examples include Celsius and Fahrenheit temperature, date of birth.
ratio scale – a ratio is an interval scale with a true zero point, so that ratios between values are meaningfully defined. Examples are absolute temperature, weight, height, blood count, and income, as in each case it is meaningful to speak of one value as being so many times greater or less than another value.

Question 113

measures of central tendency

Answer 113

A general term for several values of the distribution of a set of values or measurements located at or near the middle of the set. The principal measures of central tendency are the mean, median, and mode.

Question 114

median

Answer 114

The value in a set of ranked observations that divides the data into two parts of equal size. When there is an odd number of observations the median is the middle value. When there is an even number of observations the measure is calculated as the average of the two central values. Provides a measure of location of a sample that is suitable for asymmetric distributions and is also relatively insensitive to the presence of outliers.

Question 115

meta-analysis

Answer 115

A collection of techniques whereby the results of two or more independent studies are statistically combined to yield an overall answer to a question of interest. The rationale behind this approach is to provide a test with more power than is provided by the separate studies themselves. The procedure has become increasingly popular in the last decade or so but it is not without its critics particularly because of the difficulties of knowing which studies should be included and to which population final results actually apply.

Question 116

mode

Answer 116

The most frequently occurring value in a set of observations. Occasionally used as a measure of location.

Question 117

multicollinearity

Answer 117

in multiple regression analysis, a situation in which at least some of the independent variables are highly correlated with each other. Such a situation can result in inaccurate estimates of the parameters in the regression model.

Question 118

multinomial distribution

Answer 118

the probability distribution associated with the classification of each of a sample of individuals into one of several mutually exclusive and exhaustive categories. When the number of categories is two, the distribution is called binomial.

Question 119

multiple comparison test

Answer 119

Procedures for detailed examination of the differences between a set of means, usually after a general hypothesis that they are all equal has been rejected. No single technique is best in all situations and a major distinction between techniques is how they control the possible inflation of the type I error.

Question 120

multiple regression

Answer 120

A term usually applied to models in which a continuous response variable, y, is regressed on a number of explanatory variables, x1,x2,….xq.

Question 121

multivariate analysis

Answer 121

a set of techniques used when the variation in several variables has to be studied simultaneously. In statistics any analytic method that allows the simultaneous study of two or more dependent variables.

Question 122

multivariate data

Answer 122

Data for which each observation consists of values for more than one random variable. For example, measurements on blood pressure, temperature and heart rate for a number of subjects.

Question 123

mutually exclusive events

Answer 123

Events that cannot occur jointly.

Question 124

nominal scale

Answer 124

classification into unordered qualitative categories, e.g. race, religion, country of birth. Measurements of individual attributes are purely nominal scales, as there is no inherent order to their categories.

Question 125

nonparametric method (distribution fee methods)

Answer 125

Statistical techniques of estimation and inference that are based on a function of the sample observations, the probability distribution of which does not depend on a complete specification of the probability distribution of the population from which the sample was drawn. Consequently the techniques are valid under relatively general assumptions about the underlying population. Often such methods involve only the ranks of the observations rather than the observations themselves. Examples are Wilcoxon’s signed rank test and Friedman’s two way analysis of variance. In many cases these tests are only marginally less powerful than their analogues which assume a particular population distribution (usually a normal distribution), even when that assumption is true. Also commonly known as nonparametric methods although the terms are not completely synonymous.

Question 126

nonrandomized clinical trial

Answer 126

A clinical trial in which a series of consecutive patients receive a new treatment and those that respond (according to some pre-defined criterion) continue to receive it. Those patients that fail to respond receive an alternative, usually the conventional, treatment. The two groups are then compared on one or more outcome variables. One of the problems with such a procedure is that patients who respond may be healthier than those who do not respond, possibly resulting in an apparent but not real benefit of treatment.

Question 127

normal distribution

Answer 127

A probability distribution, f(x), of a random variable, X, that is assumed by any statistical methods.

Question 128

null hypothesis

Answer 128

The ‘no difference’ or ‘no association’ hypothesis to be tested (usually by means of a significance test) against an alternative hypothesis that postulates non-zero difference or association.

Question 129

observational study

Answer 129

A study in which the objective is to uncover cause-and-effect relationships but in which it is not feasible to use controlled experimentation, in the sense of being able to impose the procedure or treatments whose effects it is desired to discover, or to assign subjects at random to different procedures. Surveys and most epidemiologic studies fall into this class. Since the investigator does not control the assignment of treatments there is no way to ensure that similar subjects receive different treatments. The classical example of such a study that successfully uncovered evidence of an important causal relationship is the smoking and lung cancer investigation of Doll and Hill.

Question 130

observer variation (error)

Answer 130

variation (or error) due to failure of the observer to measure or identify a phenomenon accurately. Observer variation erodes scientific credibility whenever it appears. There are two varieties of observer variation: interobserver variation, i.e. the amount observers vary from one another when reporting on the same material, and intraobserver variation, i.e. the amount one observer varies between observations when reporting more than once on the same material.

Question 131

odds

Answer 131

the ratio of the probability of occurrence of an event to that of nonoccurrence (a binary variable), or the ratio of the probability that something is so to the probability that it is not so.

Question 132

odds ratio (OR)

Answer 132

The ratio of two odds for a binary variable in two groups of subjects, for example, males and females. If the two possible states of the variable are labeled ‘success’ and ‘failure’ then the odds ratio is a measure of the odds of a success in one group relative to that in the other. When the odds of a success in each group are identical then the odds ratio is equal to one. Usually estimated as ad/bc

Question 133

one-tailed test (one-sided test)

Answer 133

A significance test for which the alternative hypothesis is directional; for example, that one population mean is greater than another. The choice between a one-sided and two-sided test must be made before any test statistic is calculated.

Question 134

ordinal scale

Answer 134

classification into ordered qualitative categories, e.g. grade, where the values have a distinct order but their categories are qualitative in that there is no natural (numerical) distance between their possible values.

Question 135

outliers

Answer 135

observations differing so widely from the rest of the data as to lead one to suspect that a gross error may have been committed, or suggesting that these values come from a different population. Statistical handling of outliers varies and is difficult.

Question 136

paired t-test (matched pair t-test)

Answer 136

A Student’s t-test for the equality of the means of two populations, when the observations arised as paired samples. The test is based on the differences between the observations of the matched pairsv

Question 137

Parameter

Answer 137

A numerical characteristic of a population or a model. The probability of a ‘success’ in a binomial distribution, for example.

Question 138

parametric test

Answer 138

a statistical test that depends upon assumptions about the distribution of the data, e.g. that the data are normally distributed.

Question 139

percentage

Answer 139

a way of expressing a number as a fraction of 100 (per cent meaning “per hundred”).

Question 140

Percentile

Answer 140

The set of divisions that produce exactly 100 equal parts in a series of continuous values, such as blood pressure, weight, height, etc. Thus a person with blood pressure above the 80th percentile has a greater blood pressure value than over 80% of the other recorded values.

Question 141

placebo

Answer 141

A treatment designed to appear exactly like a comparison treatment, but which is devoid of the active component.

Question 142

point estimate (estimation)

Answer 142

The process of providing a numerical value for a population parameter on the basis of information collected from a sample. If a single figure is calculated for the unknown parameter the process is called point estimation. If an interval is calculated which is likely to contain the parameter, then the procedure is called interval estimation.

Question 143

Poisson distribution

Answer 143

The probability distribution of the number of occurrences, X, of some random event, in an interval of time or space

Question 144

population

Answer 144

In statistics this term is used for any finite or infinite collection of ‘units’, which are often people but may be, for example, institutions, events, etc.

Question 145

post hoc comparisons

Answer 145

Analyses not explicitly planned at the start of a study but suggested by an examination of the data. Such comparisons are generally performed only after obtaining a significant overall F value.

Question 146

power

Answer 146

The probability of rejecting the null hypothesis when it is false. Power gives a method of discriminating between competing test of the same hypothesis, the test with the higher power being preferred. It is also the basis of procedures for estimating the sample size needed to detect an effect of a particular magnitude. Mathematically, power is 1-β (type II error).

Question 147

predictive value

Answer 147

In screening and diagnostic tests, the probability that a person with a positive test is a true positive (i.e., does have the disease) is referred to as the “predictive value of a positive test.” The predictive value of a negative test is the probability that a person with a negative test does not have the disease. The predictive value of a screening test is determined by the sensitivity and specificity of the test, and by the prevalence of the condition for which the test is used.

Question 148

predictive value of a negative test

Answer 148

the probability that a person with a negative test does not have the disease.

Question 149

predictive value of a positive test

Answer 149

the probability that a person with a positive test is a true positive (i.e. does have the disease).

Question 150

prevalence

Answer 150

A measure of the number of people in a population who have a particular disease at a given point in time. Can be measured in two ways, as point prevalence (# of cases at a particular moments/population at a particular moment) and period prevalence (# of cases during a specified time period/# in population at midpoint of period). Essentially measure the existence of a disease.

Question 151

principal component analysis

Answer 151

a statistical method to simplify the description of a set of interrelated variables. Its general objectives are data reduction and interpretation; there is no separation into dependent and independent variables; the original set of correlated variables is transformed into a smaller set of uncorrelated variables called the principal components. Often used as the first step in a factor analysis.

Question 152

probability

Answer 152

A measure associated with an event A and denoted by Pr(A) which takes a value such that 0 ≤ Pr(A) ≤ 1. Essentially the quantitative expression of the chance than an event will occur. In general the higher the value of Pr(A) the more likely It is that the event will occur. If the event cannot happen Pr(A) = 0; if an event is certain to happen Pr(A) = 1. Numerical values can be assigned in simple cases by one of the following two methods:

If the sample space can be divided into subsets of n (n ≥ 2) equally likely outcomes and the event A is associated with r (0 ≤ r ≤ n) of these, then Pr(A) = r / n.
If an experiment can be repeated a large number of times, n, and in r cases the event A occurs, then r / n is called the relative frequency of A. If this leads to a limit as n ? 8, this limit is Pr(A).

Question 153

probability distribution

Answer 153

For a discrete random variable, a mathematical formula that gives the probability of each value of the variable. See, for example, binomial distribution and Poisson distribution. For a continuous random variable, a curve described by a mathematical formula which specifies, by ways of areas under the curve, the probability that the variable falls within a particular interval. Examples include the normal distribution and the exponential distribution. In both cases the term probability density may also be used. (A distinction is sometimes made between ‘density’ and ‘distribution’, when the latter is reserved for the probability that the random variable falls below some value. In this dictionary, however, the latter will be termed the cumulative probability distribution and probability distribution and probability density used synonymously.

Question 154

proportion

Answer 154

A type of ratio in which the numerator is included in the denominator.

Question 155

proportional hazards model (Cox’s proportional hazards)

Answer 155

A method that allows the hazard function to be modeled on a set of explanatory variables without making restrictive assumptions about the dependence of the hazard function on time. The model involved is

ln h(t) = ln α(t) + β1x1+β2x2+…+βqxq

where x1, x2, …,xq are the explanatory variables of interest, and h(t) the hazard function. The so-called baseline hazard function, a(t), is an arbitrary function of time. For any two individuals at any point in time the ratio of the hazard functions is a constant. Because the baseline hazard function, a(t), does not have to be specified explicitly, the procedure is essentially a distribution free method. Estimates of the parameters in the model, i.e. ß1, ß2,…,ßq are usually obtained by maximum likelihood estimation, and depend only on the order in which events occur, not on the exact times of their occurrence.

Question 156

prospective study (cohort study)

Answer 156

Studies in which individuals are followed-up over a period of time. A common example of this type of investigation is where samples of individuals exposed and not exposed to a possible risk factor for a particular disease, are followed forward in time to determine what happens to them with respect to the illness under investigation. At the end of a suitable time period a comparison of the incidence of the disease amongst the exposed and non-exposed is made. A classical example of such a study is that undertaken among British doctors in the 1950s, to investigate the relationship between smoking and death from lung cancer. All clinical trials are prospective.

Question 157

P-value

Answer 157

the probability that a test statistic would be as extreme as or more extreme than observed if the null hypothesis were true.

Question 158

qualitative data

Answer 158

1. observations or information characterized by measurement on a categorical scale, i.e. a dichotomous (non-numeric) or nominal scale, or if the categories are ordered, an ordinal scale. Examples are sex, hair color, death or survival. 2. systematic non-numerical observations by sociologists, anthropologists, etc. using approved methods such as participant observation or key informants.

Question 159

quantiles

Answer 159

Divisions of a probability distribution or frequency distribution into equal, ordered subgroups, for example, quartiles or percentiles.

Question 160

quartile

Answer 160

The values that divide a frequency distribution or probability distribution into four equal parts.

Question 161

random error or variation

Answer 161

The variation in a data set unexplained by identifiable sources.

Question 162

randomization (randomized experiment)

Answer 162

Allocation of individuals to groups, e.g., for experimental and control regimens, by chance.

Question 163

randomized controlled trial (RCT)

Answer 163

an epidemiologic experiment in which subjects in a population are randomly allocated into groups, usually called study and control groups, to receive or not receive an experimental preventive or therapeutic procedure, maneuver, or intervention. The results are assessed by rigorous comparison of rates of disease, death, recovery, or other appropriate outcome in the study and control groups. RCTs are generally regarded as the most scientifically rigorous method of hypothesis testing available in epidemiology.

Question 164

random sample

Answer 164

Either a set of n independent and identically distributed random variables, or a sample of n individuals selected from a population in such a way that each sample of the same size is equally likely.

Question 165

random variable

Answer 165

A variable, the values of which occur according to some specified probability distribution.

Question 166

range

Answer 166

The difference between the largest and smallest observations in a data set. Often used as an easy-to-calculate measure of the dispersion in a set of observations but not recommended for this task because of its sensitivity to outliers and the fact that its value increases with sample size.

Question 167

ranks

Answer 167

The relative positions of the members of a sample with respect to some characteristic.

Question 168

rate

Answer 168

A measure of the frequency of some phenomenon of interest given by # of events in a specified period/avg. population during the period

Question 169

ratio

Answer 169

The value obtained by dividing one quantity by another: a general term of which rate, proportion, percentage, etc., are subsets. The important difference between a proportion and a ratio is that the numerator of a proportion is included in the population defined by the denominator, whereas this is not necessarily so for a ratio.

Question 170

receiver operating characteristic (ROC or relative operating characteristic) curve

Answer 170

a graphic means for assessing the ability of a screening test to discriminate between healthy and diseased persons. The term receiver operating characteristic comes from psychometry, where the characteristic operating response of a receiver-individual to faint stimuli or nonstimuli was recorded.

Question 171

regression

Answer 171

As used by Francis Galton (1822-1911) one of the founders of modern biology and biometry, in his book Hereditary Genius (1869), this meant the tendency of offspring of exceptional parents to possess characteristics closer to the average for the general population. Hence “regression to the mean,” i.e. the tendency of individuals at the extremes to have values nearer to the mean on repeated measurement. Can also be a synonym for regression analysis in statistics.

Question 172

regression analysis

Answer 172

given data on a dependent variable y and one or more independent or predictor variables x1, x2, etc., regression analysis involves finding the “best” mathematical model (within some restricted class of models) to describe y as a function of the x’s, or to predict y from the x’s. The most common form is a linear model; in epidemiology, the logistic and proportional hazards models are also common.

Question 173

regression coefficient (multiple regression)

Answer 173

A term usually applied to models in which a continuous response variable, y, is regressed on a number of explanatory variables, x1, x2,…,xq. Explicitly the model fitted is

E (y) = β0+β1x1+β2x2+…+βqxq

the model for n observations can be written as
where contains the residual error terms and . Least squares estimation of the parameters involves the following set of equations

The regression coefficients ß1, ß2,…,ßq give the change in the response variable corresponding to a unit change in the appropriate explanatory variable, conditional on the other variables remaining constant. Significance tests of whether the coefficients take the value zero can be derived on the assumption that for a given set of values of the explanatory variables, y has a normal distribution with constant variance.

Question 174

relative risk (RR or risk ratio)

Answer 174

A measure of the association between exposure to a particular factor and risk of a certain outcome, calculated as incidence rate among exposed/incidence rate among nonexposed. Thus a relative risk of 5, for example, means that an exposed person is 5 times as likely to have the disease than one who is not exposed. Relative risk does not measure the probability that someone with the factor will develop the disease. The disease may be rare among both the nonexposed and the exposed.

Question 175

reliability

Answer 175

The extent to which the same measurements of individuals obtained under different conditions yield similar results. Reliability refers to the degree to which the results obtained by a measurement, procedure can be replicated. Lack of reliability may arise from divergences between observers or instruments of measurement or instability of the attribute being measured.

Question 176

repeated-measures design

Answer 176

Repeated measures is a type of analysis of variance that generalizes Student’s t test for paired samples. It is used when two or more measurements of the same type are made on the same subject. Analysis of variance is characterized by the use of factors, which are composed of levels. Repeated measures analysis of variance involves two types of factors–between subjects factors and within subjects factors. The repeated measures make up the levels of the within subjects factor. For example, suppose each subject has his/her reaction time measured under three different conditions. The conditions make up the levels of the within subjects factor. Depending on the study, subjects may divided into groups according to levels of other factors called between subjects factors. Each subject is observed at only a single level of a between-subjects factor. For example, if subjects were randomized to aeorbic or stretching exercise, form of exercise would be a between-subjects factor. The levels of a within-subject factor change as we move within a subject, while levels of a between-subject factor change only as we move between subjects.

Question 177

Residual

Answer 177

The difference between the observed value of a response variable (yi) and the value predicted by some model of interest ( ). Examination of a set of residuals, usually by informal graphical techniques, allows the assumptions made in the model fitting exercise, for example, normality, homogeneity of variance, etc., to be checked. Generally, discrepant observations have large residuals, but some form of standardization may be necessary in many situations to allow identification of patterns among the residuals that may be a cause for concern.

Question 178

response variable

Answer 178

The variable of primary importance in investigations since the major objective is usually to study the effects of treatment and/or other explanatory variables on this variable and to provide suitable models for the relationship between the explanatory variables.

Question 179

retrospective study

Answer 179

A general term for studies in which all the events of interest occur prior to the onset of the study and findings are based on looking backward in time. Most common is the case-control study, in which comparisons are made between individuals who have a particular disease or condition (the cases) and individuals who do not have the disease (the controls). A sample of cases is selected from the population of individuals who have the disease of interest and a sample of controls is taken from among those individuals known not to have the disease. Information about possible risk factors for the disease is then obtained retrospectively for each person in the study by examining past records, by interviewing each person and/or interviewing their relatives, or in some other way. In order to make the cases and controls otherwise comparable, they are frequently matched on characteristics known to be strongly related to both disease and exposure leading to a matched case-control study. Age, sex and socioeconomic status are examples of commonly used matching variables. Also commonly encountered is the retrospective cohort study, in which a past cohort of individuals are identified from previous information, for example, employment records, and their subsequent mortality or morbidity determined and compared with the corresponding experience of some suitable control group.

Question 180

risk factor

Answer 180

An aspect of persona behavior or lifestyle, an environmental exposure, or an inborn or inherited characteristic which is thought to be associated with a particular disease or condition.

Question 181

risk ratio

Answer 181

The ratio of two risks, usually exposed/not exposed.

Question 182

sample

Answer 182

a selected subset of a population. A sample may be random or nonrandom and may be representative or nonrepresentative. Several types of samples exist:
area sample – a method of sampling that can be used when the numbers in the population are unknown. The total area to be sampled is divided into subareas, e.g. by means of a grid that produces squares on a map; these subareas are then numbered and sampled, using a table of random numbers.
cluster sample – each unit selected is a group of persons (all persons in a city block, a family, a school, etc.) rather than an individual.
grab sample (sample of convenience) – samples selected by easily employed but basically nonprobabilistic methods. It is improper to generalize from the results of a survey based upon such a sample, for there is no way of knowing what types of bias may have been present.
probability (random) sample –all individuals have a known chance of selection. They may all have an equal chance of being selected, or, if a stratified sampling method is used, the rate at which individuals from several subsets are sampled can be varied so as to produce greater representation of some classes than others.
simple random sample – a form of sampling design in which n distinct units are selected from the N units in the population in such a way that every possible combination of n units is equally likely to be the sample selected. With this type of sampling design the probability that the ith population unit is included in the same, so that the inclusion probability is the same for each unit. Designs other than this one may also give each unit equal probability of being included, both other here does each possible sample of n units have the same probability.
stratified random sample – this involves dividing the population into distinct subgroups according to some important characteristic, such as age or socioeconomic status, and selecting a random sample out of each subgroup. If the proportion of the sample drawn from each of the subgroups or strata, is the same as the proportion of the total population contained in each stratum, then all strata will be fairly represented with regard to numbers of persons in the sample.
systematic sample – the procedure of selecting according to some simple, systematic rule, such as all persons whose names begin with specified alphabetic letters, born on certain dates, or located at specified points on a list. A systematic sample may lead to errors that invalidate generalizations.

Question 183

sampling distribution

Answer 183

The probability distribution of a statistic calculated from a random sample of a particular size. For example, the sampling distribution of the arithmetic mean of samples of size n taken from a normal distribution with mean μ with standard deviation s, is a normal distribution also with mean μ but with standard deviation .

Question 184

scatterplot (Synonym for scatter diagram)

Answer 184

A two-dimensional plot of a sample of bivariate observations. The diagram is an important aid in assessing what type of relationship links the two variables. An example is shown in below.

Question 185

sensitivity

Answer 185

An index of the performance of a diagnostic test, calculated as the percentage of individuals with a disease who are correctly classified as having the disease, i.e. the conditional probability of having a positive test result given having the disease. A test is sensitive to the disease if it is positive for most individuals having the disease where: a. diseased individuals detected by the test (true positives)

b. nondiseased individuals positive by the test (false positives)
c. diseased individuals not detectable by the test (false negatives)
d. nondiseased individuals negative by the test (true negatives)

Sensitivity = a/(a + c) 
Specificity = d/(b + d)

Predictive value (positive test result) = a/(a + b)
Predictive value (negative test result) = d/(c + d)3

Question 186

Specificity

Answer 186

An index of the performance of a diagnostic test, calculated as the percentage of individuals without the disease who are classified as not having the disease, i.e. the conditional probability of a negative test result given that the disease is absent. A test is specific if it is positive for only a small percentage of those without the disease.

Question 187

Slope

Answer 187

used to describe the measurement of the steepness, incline, gradient, or grade of a straight line. A higher slope value indicates a steeper incline. The slope is defined as the ratio of the “rise” divided by the “run” between two points on a line, or in other words, the ratio of the altitude change to the horizontal distance between any two points on the line. The slope of a line in the plane containing the x and y axes is generally represented by the letter m, and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line. This is described by the following equation:

m = Δy / Δx

If y is a linear function of x, then the coefficient of x is the slope of the line created by plotting the function. Therefore, if the equation of the line is given in the form y = mx + b then m is the slope. This form of a line’s equation is called the slope-intercept form, because b can be interpreted as the y-intercept of the line, the y-coordinate where the line intersects the y-axis.

Question 188

standard deviation

Answer 188

A measure of dispersion or variation. The most commonly used measure of the spread of a set of observations. Equal to the positive square root of the variance.

Question 189

standard error (SE)

Answer 189

The standard deviation of the sampling distribution of a statistic. For example, the standard error of the sample mean of n observations is where s2 is the variance of the original observations.

Question 190

standardization

Answer 190

A set of techniques used to remove as much as possible the effects of age or other confounding variables when comparing two or more populations. The common method uses weighted averaging of rates of age, sex or some other confounding variable(s) according of some specified distribution of these variables.

Question 191

statistic

Answer 191

A numerical characteristic of a sample. For example, the sample mean and sample variance.

Question 192

statistical significance

Answer 192

Statistical methods allow an estimate to be made of the probability of the observed or greater degree of association between independent and dependent variables under the null hypothesis. From this estimate, in a sample of given size, the statistical “significance” of a result can be stated. Usually the level of statistical significance is stated by the p value.

Question 193

Statistical test

Answer 193

a procedure that is intended to decide whether a hypothesis about the distribution of one or more populations or variables should be rejected or accepted. Statistical tests may be parametric or nonparametric.

Question 194

stem and leaf plot

Answer 194

A method of displaying data in which each observation is split into two parts labeled the ‘stem’ and the ‘leaf’. A tally of the leaves corresponding to each stem ahs the shape of a histogram but also retains the actual observation values.

Question 195

stepwise regression (selection models in regression)

Answer 195

A series of methods for selecting ‘good’ (although not necessarily the best) subsets of explanatory variables when using regression analysis. The three most commonly used of these methods are forward selection, backward elimination and a combination of both of these known as stepwise regression. The criterion used for assessing whether or not a variable should be added to an existing model in forward selection or removed from an existing model in backward elimination is, essentially, the change in the residual sum-of-squares produced by the inclusion or exclusion of the variable.

Question 196

subjective probability (personal probability)

Answer 196

A radically different approach to allocating probabilities to events than, for example, the commonly used long-term relative frequency approach. In this approach, probability represents a degree of belief in a proposition, based on all the information. Two people with different information and different subjective ignorance may therefore assign different probabilities to the same proposition. They only constraint is that a single person’s probabilities should not be consistent.

Question 197

sums of squares

Answer 197

a concept in inferential statistics and descriptive statistics. More properly, it is “the sum of the squared deviations”. Mathematically, it is an unscaled, or unadjusted measure of variability. When scaled for the number of degrees of freedom, it estimates the variance, or spread of the observations about their mean value. The distance from any point in a collection of data, to the mean of the data, is the deviation

Question 198

Survey

Answer 198

an investigation in which information is systematically collected but in which the experimental method is not used. A population survey may be conducted by face-to-face inquiry, self-completed questionnaires, telephone, postal service, or in some other way.

Question 199

survival analysis

Answer 199

a class of statistical procedures for estimating the survival function and for making inferences about the effects on it of treatments, prognostic factors, exposures, and other covariates.

Question 200

symmetric distribution

Answer 200

A probability distribution or frequency distribution that is symmetrical about some central value.

Question 201

target population

Answer 201

The collection of individuals, items, measurements, etc., about which it is required to make inferences. Often the population actually sampled differs from the target population and this may result in misleading conclusions being made. The target population requires a clear precise definition, and that should include the geographical area (country, region, town, etc.) if relevant, the age group and gender.

Question 202

test statistic

Answer 202

A statistic used to assess a particular hypothesis in relation to some population. The essential requirement of such a statistic is known a distribution when the null hypothesis is true.

Question 203

transformation

Answer 203

A change in the scale of measurement for some variable(s). Examples are the square room transformation and logarithm transformation.

Question 204

t-test (T-distribution)

Answer 204

the t-distribution is the distribution of a quotient of independent random variables, the numerator of which is a standard normal variate and the denominator of which is the positive square root of the quotient of a chi-square distributed variate and its number of degrees of freedom. The t-test uses a statistic that, under the null hypothesis, has the t-distribution to test whether two means differ significantly, or to test linear regression or correlation coefficients.

Question 205

two-sample t-test

Answer 205

a hypothesis test for answering questions about the mean where the data are collected from two random samples of independent observations, each from an underlying normal distribution

Question 206

two-tailed test

Answer 206

a statistical significance test based on the assumption that the data are distributed in both directions from the central value(s).

Question 207

two-way analysis of variance (factorial AOV)

Answer 207

The two-way analysis of variance is an extension to the one-way analysis of variance. There are two independent variables (hence the name two-way). The two independent variables in a two-way ANOVA are called factors. The idea is that there are two variables, or factors, which affect the dependent variable. Each factor will have two or more levels within it, and the degrees of freedom for each factor is one less than the number of levels. The same assumptions apply for one-way analysis of variance.

Question 208

Type I error

Answer 208

The error of rejecting a true null hypothesis; i.e. declaring a difference exists when it does not.

Question 209

Type II error

Answer 209

the error of failing to reject a false null hypothesis; i.e. declaring a difference does not exist when it in fact does.

Question 210

unbiased (bias)

Answer 210

In general terms, deviations of results or inferences from the truth, or processes leading to such deviation. More specifically, the extent to which the statistical method used in a study does not estimate the quantity thought to be estimated, or does not test the hypothesis to be tested. In estimated usually measured by the difference between a parameter estimate and its expected value. An estimator for which is said to be unbiased.

Question 211

Variable

Answer 211

Some characteristic that differs from subject to subject or from time to time. Any attribute, phenomenon, or event that can have different values.

Question 212

variance

Answer 212

In a population, the second moment about the mean

Question 213

weighted average

Answer 213

An average of quantities to which have been attached a series of weights in order to make proper allowance for their relative importance

Question 214

weighted sample

Answer 214

a sample that is not strictly proportional to the distribution of classes in the universe population. A weighted sample has been adjusted to include larger proportions of some than other parts of the population because those parts accorded greater “weight” would otherwise not have sufficient numbers in the sample to lead to generalizable conclusions, or because they are considered to be more important, more interesting, more worthy of detailed study or other reasons.

Question 215

z-score (standard scores)

Answer 215

Variable values transformed to zero mean and unit variance.

Question 216

z-test

Answer 216

A test for assessing hypotheses about population means when their variances are known

Question 217

z-transformation (Fisher’s Z transformation)

Answer 217

A transformation of Pearson’s product moment correlation coefficient, r, give by

z = 1/2 ln [(1+r)/(1-r)]

The statistic z has a normal distribution with mean

z = 1/2 ln [(1+p)/(1-p)]

where p is the population correlation value and variance 1/(n-3) where n is the sample size. The transformation may be used to test hypotheses and to construct confidence intervals for p.